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lfunc_lfunctions • Show schema
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{'Lhash': '197345683381066200627084929105', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7922869913932613, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.7922869913932613, 2.5243377989621387], 'a8': [0, 0], 'a9': [-2.3722813232690143, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.358112565958518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.7922869913932613, -2.5243377989621387]]]], 'bad_primes': [2, 5, 7], 'central_character': '2800.2351', 'coefficient_field': 'CDF', 'conductor': 2800, 'conductor_radical': 70, 'conjugate': '2071848193601512270623256946509', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7922869913932613, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7922869913932613, -2.5243377989621387]], [[1.0, 0], [0, -0.7922869913932613], [-11.0, 0]], [[1.0, 0], [0, -5.372281323269014], [-13.0, 0]], [[1.0, 0], [0, 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'1.14538804912830646473759777608839', '2.92719002272856136711579585722320', '3.31453369834933869677226052713868', '4.61455816223052971347908095713447', '5.32120767684463593591394601886606', '6.06619796236144133213621445224151', '6.81331600538590722761882877823053', '7.81302026346778224881572687079884', '8.098113230914259639240293667937997'], 'prelabel': '2-2800-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.728436587917672, 'root_angle': 0.9301386238306848, 'root_number': '-0.97601167068573990917828330645163312095016158077628994808 + 0.21771820935610965024394780557223051033602801756669963278*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4650693119153424', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15567829443344706866585458359', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.14538804912830646473759777609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92719002272856136711579585722', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.358112565958518, 'bad_primes': [2, 5, 7], 'central_character': '28.27', 'conductor': 2800, 'conductor_radical': 70, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2800/2/k/l/2351/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-2800-28.27-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2800-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.728436587917672, 'root_angle': 0.4650693119153424, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.15567829443344706866585458359', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '197345683381066200627084929105', 'Lhash_array': ['197345683381066200627084929105'], 'label': '2-2800-28.27-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2800/2/k/l/2351/4'}